No -- what I was going for was +/- 100mV or so. Any more accuracy is not required for basic checks when you have equipment that already works and you can take measurements as a baseline. All the OP needs to do is take measurements of the what he has while it's working, and note the results. The differences are what's important when something strange happens.
That's a reasonable strategy when the initial state is known, or highly likely to be, good - look for deviation from the norm and investigate should it arise.
Given the OP's question about the requirement for a battery tester when using a Pila charger and AW cells, I agree that it's not a requirement to have lab grade testing equipment in order to monitor for undesirable changes, especially since both Pila and AW products have earned the respect they have.
I'd still prefer to establish the baseline for correct operation of the charger with a more accurate meter, but I'll concede it's not really necessary.
As for my reference to +/- 5mV... If you're simply aiming to get an idea of state of charge of a battery, then +/- 100mV is fine. I was also considering the question of correct (safe) termination voltage when charging LiIon cells, which apparently requires tighter tolerances.
I'm fundamentally in agreement with TTA. (BTW, when I checked yesterday, there weren't any of the inexpensive voltage references available on the 'Bay, though there likely will be again).
It's not necessary to buy a Fluke to check batteries (and a Fluke isn't going to be automatically and permanently absolutely correct). Many less expensive meters will be stable and accurate enough, especially if they can be verified against a known-good reference of the required accuracy.
- Syncytial.